But with fiat currencies one can morally justify accepting most cash (such as supermarket money etc...) without much thought because one can assume (possibly falsely) that there are some kind of checks and balances behind it.

Ben is going to print $1 Trillion this year to buy UST's and MBS's so that his banking friends can continue to make record bonuses.

our Fed gov't is going to run another $1 Trillion in deficit spending so that they can continue to remain in office and fund their pet programs.

If you look in the Marketplace, there are a few individuals who are very clearly conducting money laundering operations with Bitcoin. To the users of this forum's credit (and moderators) these are generally highlighted in big bold red letters that these are money laundering operations.

To answer your question, if I am aware that a transaction is being done to further illegal activities (like in the example above) then I would not conduct the transaction. For the most part, you just need to use common sense and intuition. Like the old saying, if it's too good to be true, it probably is. There will be cases where people will unknowingly conduct transactions with those who are engaging in illegal activities but as mentioned, this happens with all currencies.

Let's suppose someone offers to sell you some bitcoins at a good price, do you feel you have any obligation to know where the bitcoins came from?

It depends on how you define 'good price'. Is it at market price, 5% below, 10% below ? No serious trader would do a trade where he loses out a lot on the trade. So personally, if somebody got in touch with me and said they wanted to do a larger transaction with a 15% surcharge, my alarm bells would ring. I am sure though, that some traders would not hesitate to the deal, as many are greedy. I would simply decline such a person. If he however said that he was willing to pay something reasonable like a 3-5% surcharge, then I would be more interested. So the answer is that I would simply decline the transaction if I felt something was fishy.

For example let's say a terrorist group in the Middle East buys or mines bitcoins, send them a cell in the USA. The cell member trades them with you for cash, and then uses the cash to buy bomb parts to blow up a building killing 100s of people.

Yes, as money or bitcoins is only tools, you have no responsibility to check anything at all, unless of course there's some reasons to be very suspicious for whatever reason. If there comes one scary man, and he lays out plans on the table and goes on about how he's going to bomb a building, then I think it's time to call the police. But I don't see that happening!

Would you feel any remorse or would you just feel like it was nothing to do with you? And if you would feel remorseful do you feel that you have any obligation to inquiry before you buy the coins as to where they came from and how the owner got them?

I know of people that have rejected trades for various reasons. I heard one trader rejected an otc deal because the other party bluntly stated he was a drug dealer. In another event the money in question was the results of a heist where cash was stolen, so the trader in question would not accept the cash deposit from the thief.

Some people are just plain stupid and tell outright they're involved in crime, then if you're a legitimate trader, you don't deal with such people.

I want to know how the OP even come up with an idea as sick as "building a dungeon for 2 year olds" ... I mean really?

Do we really have to drag out the absolute worst in humanity in attempts to smear bitcoin?

So OP how much do you know about dungeons for 2 year olds, you seem to have some background knowledge or interest in such disgusting ideas? Why is that I wonder? What exactly are your motivations for bringing up such an evil thought?

Passing blame onto bitcoins (or the hammers used to build dungeons) for the actions of dark souls and sick minds in the realms you might inhabit is not going help with redemption or whatever else it is you might be seeking, morally speaking.

God help you, is all I can think to such a spiritually empty line of reasoning.